To begin with, we analyze the rank computation cost.
In the worst case, the dimension of matrix \(D\)  representing
a sub-quiver is \(N \times M\) , when the sub-quiver is the
same as the quiver \(Q\) .
According to Golub and Van Loan [1]} the
best known rank computation algorithms that internally
involve singular value decomposition (SVD) for a
\(N \times M\)  matrix has a time complexity of \(O(NM^2)\) .
